Exploration seismology is widely used for detecting oil and gas deposits. Seismic waves emitted at predetermined locations on a surface or in a surface layer using, for example, explosives propagate downwards into the ground. When the seismic waves encounter a boundary between different geological layers, a portion of the seismic waves is reflected back to the surface which is detected using a pre-deployed array of sensors—geophones. The non-reflected portion of the seismic waves is transmitted further downwards where it is reflected off deeper boundaries and subsequently recorded at the surface at later time instances enabling detection of multiple geological layers. The output signals of the geophones are then processed producing seismic data called “migrated sections”.
The characteristics of seismic reflections from layer boundaries are determined by geometric and acoustic properties of the layers, with the acoustic properties being expressed in terms of seismic impedances—product of layer density with propagation velocity of the seismic waves through the respective layer. The amplitude of a reflected seismic wave depends upon the amount of difference between the seismic impedances of two adjacent layers, while its polarity depends upon whether the reflected seismic wave is traveling from a layer of higher impedance to a layer of lower impedance, or vice versa. Hydrocarbon bearing layers are likely porous, lowering their density. Also, the hydrocarbons disposed therein transmit seismic waves less efficiently and, therefore, more slowly than non-porous and non-permeable materials. Both of these effects lower the seismic impedance and, therefore, hydrocarbon deposits are usually associated with enhanced impedance contrasts. As a result, seismic waves reflected from hydrocarbon bearing layers are different from seismic waves reflected from surrounding layers. However, lateral changes in reflectivity do not directly imply the presence of hydrocarbons.
Another property of the hydrocarbon bearing layers is their compressibility. Natural gas is highly compressible and oil, which typically contains natural gas dissolved therein is, to some extent, also compressible. This leads to relatively large frictional amplitude losses of seismic waves passing therethrough. For this reason, layers of this type are often described as having low “quality.” On the other hand, porous layers where hydrocarbons have been replaced by ground water cause smaller amplitude losses, since water is substantially incompressible. Therefore, seismic waves propagate further through such layers, which are then considered to have higher “quality.”
Quality is useful in hydrocarbon exploration because it is closely related to the compressibility, but, unlike the compressibility, it is an observable seismic attribute. The quality factor—or Q factor—quantifies the rate of amplitude decline via:
                                                        A              f                        ⁡                          (              t              )                                =                                                    A                f                            ⁡                              (                0                )                                      ⁢                                                  ⁢            exp            ⁢                                                  ⁢                          (                                                                    -                    π                                    ⁢                                                                          ⁢                  ft                                Q                            )                                      ,                            (        1        )            where Af(t) denotes the local amplitude of the fth frequency at time t. According to this definition Q gives the amount of amplitude loss per wave cycle, indicating that seismic waves of shorter wavelength—i.e. higher frequencies—decline faster than seismic waves having longer wavelengths.
Amplitude, frequency, and Q factor have been extensively investigated and used in the past as separate seismic attributes. Recently, a new method for evaluating migrated sections has been developed in which all three effects are combined in a single seismic attribute, referred to informally as the “sweetness factor,” which has been found to be highly beneficial in exploration seismology. The sweetness factor is defined as the quotient of instantaneous amplitude to instantaneous frequency of a seismic trace. At present, the instantaneous amplitude and the instantaneous frequency are determined based on the Hilbert transform. Unfortunately, this method does not provide physically meaningful results in situations where the seismic trace contains events that overlap in time but have different frequencies. Such situations are frequently encountered in exploration seismology.
It would be highly desirable to overcome the above problem of the state of the art and to provide an improved method capable of determining a sweetness factor in situations when the seismic data contain events that overlap in time but have different frequencies.